Warning: Your warranty will be voided. And you could destroy your phone with this guide. I am not responsible for any damaged phone. And don't point a finger at me if you failed to solder everything properly.

Please only do this DIY if you know what you are doing. If you never used a solder iron before please DO NOT DO IT!!! The battery could explode if it gets too hot.

Let's begin
First of all prepare all the stuff you need. It's annoying if you need to search for things during the work.

To make placing of the copper foil easier, we mark the positions of the contacts with a pencil using the old battery.

Extend the markings to the top of the battery.

Skin the cables and prepare them with tin-solder. Also cut the skin ends to a suitable length.

Put your battery in a vice, but don't use too much force!

Prepare your solder iron with a thin tip and set the temperature to 400°C.

Prepare the battery with a bit of tin-solder (makes it easier and faster when you attach the cables).

Attach the cables (black -, yellow charging, red +).

Cut the copper foil that it fits your markings. And 3 different lengths, make sure that the longest copper strip is outside facing.

Solder the cables to it, use your old battery to check if your contacts are in the right order (minus is the outside facing contact). Make sure that the cables don't cross each other, otherwise you will get a bulge in your backcover.

Check the contacts with your old battery and a multimeter. If the multimeter shows approx 3,8V between + and - aswell as + and yellow everything should be alright.

Place the battery in your phone to check if everything fits or if you need to adjust something.

If everything fits and you are sure that you have the cabling correct. Try to power on the phone.

If that worked you can apply the heat shrink. Make sure that you isolate the original contacts of the battery.

Finally check if your phone charges.

If you did a good job and used thin cables the cover does still fit and does not have a bad bulge. Mine has a small one not really noticeable (at least better than my thickened battery ).

Screenshots of CSD Tool after the fix (phone was charging that's why the discharge test fails):